Current understanding of higher-order topological insulators (HOTIs) is based primarily on crystalline materials. Here, we propose that HOTIs can be realized in quasicrystals. Specifically, we show ...that two distinct types of second-order topological insulators (SOTIs) can be constructed on the quasicrystalline lattices (QLs) with different tiling patterns. One is derived by using a Wilson mass term to gap out the edge states of the quantum spin Hall insulator on QLs. The other is the quasicrystalline quadrupole insulator (QI) with a quantized quadrupole moment. We reveal some unusual features of the corner states (CSs) in the quasicrystalline SOTIs. We also show that the quasicrystalline QI can be simulated by a designed electrical circuit, where the CSs can be identified by measuring the impedance resonance peak. Our findings not only extend the concept of HOTIs into quasicrystals but also provide a feasible way to detect the topological property of quasicrystals in experiments.
We report experimental realization of a quantum time quasicrystal and its transformation to a quantum time crystal. We study Bose-Einstein condensation of magnons, associated with coherent spin ...precession, created in a flexible trap in superfluid ^{3}He-B. Under a periodic drive with an oscillating magnetic field, the coherent spin precession is stabilized at a frequency smaller than that of the drive, demonstrating spontaneous breaking of discrete time translation symmetry. The induced precession frequency is incommensurate with the drive, and hence, the obtained state is a time quasicrystal. When the drive is turned off, the self-sustained coherent precession lives a macroscopically long time, now representing a time crystal with broken symmetry with respect to continuous time translations. Additionally, the magnon condensate manifests spin superfluidity, justifying calling the obtained state a time supersolid or a time supercrystal.
The plane problem of two‐dimensional decagonal quasicrystals with a rigid circular arc inclusion was investigated under infinite tension and concentrated force. Based on complex representations of ...stresses and displacements of two‐dimensional decagonal quasicrystals, the above problem is transformed into Riemann boundary problem by using the analytic continuation principle of complex functions. The general solutions of two‐dimensional decagonal quasicrystals under the action of plane concentrated force and infinite uniform tension are derived. The closed solutions of complex potential functions in several typical cases are obtained, and the formula of singular stress field at the tip of rigid line inclusions is given. The results show that the stress field at the tip of circular arc rigid line inclusions has singularity of oscillation under plane load. Numerical examples are given to analyze the effects of inclusion radius, different inclusions, the coupling coefficient and phason field parameter on stress singularity coefficients.
The plane problem of two‐dimensional decagonal quasicrystals with a rigid circular arc inclusion was investigated under infinite tension and concentrated force. Based on complex representations of stresses and displacements of two‐dimensional decagonal quasicrystals, the above problem is transformed into Riemann boundary problem by using the analytic continuation principle of complex functions. The general solutions of two‐dimensional decagonal quasicrystals under the action of plane concentrated force and infinite uniform tension are derived.…
Quasicrystalline alloys and their composites have been extensively studied due to their complex atomic structures, mechanical properties, and their unique tribological and thermal behaviors. However, ...technological applications of these materials have not yet come of age and still require additional developments. In this review, we discuss the recent advances that have been made in the last years toward optimizing fabrication processes and properties of Al‐matrix composites reinforced with quasicrystals. We discuss in detail the high‐strength rapid‐solidified nanoquasicrystalline composites, the challenges involved in their manufacturing processes and their properties. We also bring the latest findings on the fabrication of Al‐matrix composites reinforced with quasicrystals by powder metallurgy and by conventional metallurgical processes. We show that substantial developments were made over the last decade and discuss possible future studies that may result from these recent findings.
Photographic slides of an aperiodic dodecagonal tiling were used as two-dimensional diffraction gratings to describe and demonstrate the basic properties of dodecagonal quasicrystals. This paper ...complements our earlier publication on Penrose (decagonal) and Ammann (octagonal) quasicrystals, where we constructed and presented the corresponding diffraction gratings.
Is quasicrystal structure analysis a never-ending story? Why is still not a single quasicrystal structure known with the same precision and reliability as structures of regular periodic crystals? ...What is the state-of-the-art of structure analysis of axial quasicrystals? The present comprehensive review summarizes the results of almost twenty years of structure analysis of axial quasicrystals and tries to answer these questions as far as possible. More than 2000 references have been screened for the most reliable structural models of pentagonal, octagonal, decagonal and dodecagonal quasicrystals. These models, mainly based on diffraction data and/or on bulk and surface microscopic images are critically discussed together with the limits and potentialities of the respective methods employed.
Despite the rapid progress in the field of the quantum spin Hall (QSH) effect, most of the QSH systems studied up to now are based on crystalline materials. Here we propose that the QSH effect can be ...realized in quasicrystal lattices (QLs). We show that the electronic topology of aperiodic and amorphous insulators can be characterized by a spin Bott index B_{s}. The nontrivial QSH state in a QL is identified by a nonzero spin Bott index B_{s}=1, associated with robust edge states and quantized conductance. We also map out a topological phase diagram in which the QSH state lies in between a normal insulator and a weak metal phase due to the unique wave functions of QLs. Our findings not only provide a better understanding of electronic properties of quasicrystals but also extend the search of the QSH phase to aperiodic and amorphous materials that are experimentally feasible.
Optics of photonic quasicrystals Vardeny, Z. Valy; Nahata, Ajay; Agrawal, Amit
Nature photonics,
03/2013, Letnik:
7, Številka:
3
Journal Article
Recenzirano
The physics of periodic systems are of fundamental importance and result in various phenomena that govern wave transport and interference. However, deviations from periodicity may result in higher ...complexity and give rise to a number of surprising effects. One such deviation can be found in the field of optics in the realization of photonic quasicrystals, a class of structures made from building blocks that are arranged using well-designed patterns but lack translational symmetry. Nevertheless, these structures, which lie between periodic and disordered structures, still show sharp diffraction patterns that confirm the existence of wave interference resulting from their long-range order. In this Review, we discuss the beautiful physics unravelled in photonic quasicrystals of one, two and three dimensions, and describe how they can influence optical transmission and reflectivity, photoluminescence, light transport, plasmonics and laser action.
This inter-disciplinary work covering the continuum mechanics of novel materials, condensed matter physics and partial differential equations discusses the mathematical theory of elasticity of ...quasicrystals (a new condensed matter) and its applications by setting up new partial differential equations of higher order and their solutions under complicated boundary value and initial value conditions. The new theories developed here dramatically simplify the solving of complicated elasticity equation systems. Large numbers of complicated equations involving elasticity are reduced to a single or a few partial differential equations of higher order. Systematical and direct methods of mathematical physics and complex variable functions are developed to solve the equations under appropriate boundary value and initial value conditions, and many exact analytical solutions are constructed. The dynamic and non-linear analysis of deformation and fracture of quasicrystals in this volume presents an innovative approach. It gives a clear-cut, strict and systematic mathematical overview of the field. Comprehensive and detailed mathematical derivations guide readers through the work. By combining mathematical calculations and experimental data, theoretical analysis and practical applications, and analytical and numerical studies, readers will gain systematic, comprehensive and in-depth knowledge on continuum mechanics, condensed matter physics and applied mathematics.
Phase transitions connect different states of matter and are often concomitant with the spontaneous breaking of symmetries. An important category of phase transitions is mobility transitions, among ...which is the well known Anderson localization
, where increasing the randomness induces a metal-insulator transition. The introduction of topology in condensed-matter physics
lead to the discovery of topological phase transitions and materials as topological insulators
. Phase transitions in the symmetry of non-Hermitian systems describe the transition to on-average conserved energy
and new topological phases
. Bulk conductivity, topology and non-Hermitian symmetry breaking seemingly emerge from different physics and, thus, may appear as separable phenomena. However, in non-Hermitian quasicrystals, such transitions can be mutually interlinked by forming a triple phase transition
. Here we report the experimental observation of a triple phase transition, where changing a single parameter simultaneously gives rise to a localization (metal-insulator), a topological and parity-time symmetry-breaking (energy) phase transition. The physics is manifested in a temporally driven (Floquet) dissipative quasicrystal. We implement our ideas via photonic quantum walks in coupled optical fibre loops
. Our study highlights the intertwinement of topology, symmetry breaking and mobility phase transitions in non-Hermitian quasicrystalline synthetic matter. Our results may be applied in phase-change devices, in which the bulk and edge transport and the energy or particle exchange with the environment can be predicted and controlled.
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